PHYSICS 197 Section 1 Chapter C6 Conservation of Angular Momentum September 13, 2017

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Conservation Laws Noether’s theorem: A symmetry principle implies an associated conservation law. Symmetry Conservation of Translation in time Energy Translation in space Momentum Rotation in space Angular Momentum Emmy Noether, German Mathematician in the early 20th century. Reflection is different from other symmetries listed here. Why? Because it is discrete, while others are continuous. Position Orientation

Quantifying Orientation Angle is unitless. By convention, always use radians (unless specified).

Angular Velocity

Velocity vs. Angular Velocity

Clicker Question C. To your right (use right hand rule).

Practice Problem

Momentum vs. Angular Momentum Definition only valid for rigid bodies (with well-defined angular velocity). Angular momentum is parallel to angular velocity only if an object is symmetric around the axis of rotation.

Symmetric Objects Consider a rectangular book (e.g. your textbook). The book is symmetric for rotations around an axis that is perpendicular to its face and goes through its center of mass. T or F? Ans: T. Every particle on one side of the axis has a corresponding particle on the other side. The book is symmetric for rotations around an axis that goes diagonally from one corner to the other. T or F? Ans: F. The particle at point A doesn’t have a corresponding particle at point B.

Moment of Inertia

Practice Problem

Impulse vs. Twirl

Force vs. Torque

Gyroscope

Gyroscope

Gyroscope

Gyroscope

Gyroscope

Gyroscopic Precession

Gyroscopic Precession

Earth’s Precession

Conservation of Angular Momentum Analogous to linear momentum conservation, The total angular momentum of an isolated system is conserved. Three classes of isolated systems: Floats in space. Functionally isolated (external interactions deliver no net torque). Involves a collision. Two types of CAM problems: Where the system that consists of a single object whose moment of inertia changes between its initial and final states. Where parts of the system having different angular momenta interact.